definition of function
Topics
About: collection
The table of contents of this article
Starting Context
- The reader knows a definition of relation.
Target Context
- The reader will have a definition of function.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\(*F\): \(\in \{\text{ the relations }\}\)
//
Conditions:
\(\forall \langle s_1, s_2 \rangle, \langle s_1, s_3 \rangle \in F (s_2 = s_3)\)
//
2: Note
Conditions means that each element of the domain has the unique corresponding element in the range.
'map' is a 'function' with a codomain, which does not necessarily equal the range: any map is a function, but a function may not be any map, but the function can be regarded to be a map if the range is regarded to be the codomain.
